The determination of size distributions in dispersions of submicrometer particles represents an important problem in physics, chemistry, biology, and engineering. The size distribution determines many bulk properties of a dispersion and provides detailed information about the mechanisms governing both the kinetics and thermodynamics of aggregation.
A number of techniques have been developed to characterize such size distributions. The most prevalent is light scattering, which has mainly been used to measure bulk properties of colloidal dispersions and aerosols. Various weighted averages of the particle size distribution may be deduced from the turbidity of the solution, or its temporal correlation function. With more polydisperse samples, it becomes increasingly difficult to characterize the distribution using these techniques. Consequently, single particle techniques which measure the distribution itself have emerged.
Resistive pulse analysis, invented by Coulter in 1949, is the most widely used single-particle sizing method. See U.S. Pat. No. 2,656,508. While commercial Coulter counters are designed for particles larger than 1 micron, a nanopar resistive pulse analyzer developed by Deblois and Bean in 1970 has been used to detect the aggregation of 235-nm latex spheres. Since the resistive pulse technique requires electrolytic solvents, it is of limited utility when salt is an experimental parameter. Alternatively, some single-particle counters measure fluorescence or scattered light intensity. Flow cytometry has combined all three detection techniques with digital signal processing and hydrodynamic focusing in an extensive effort to characterize and sort individual mammalian cell particles larger than 1 micron.
Another technique for measuring cluster size distribution of particles designated optical pulse particle size analysis is described by Bowen et al. in Kinetics of Aggregation and Gelation, F. Family, D. P. Laudau eds. Elsevier Science Publishers, 1984. Optical pulse, particle size analysis is based on a discovered relationship between low angle scattered light intensity and cluster size of uniform size particles. For such particles, the intensity of light scattered, in the low angle limit, is proportional to the square of the number of particles in a cluster. This "n.sup.2 dependence" (where n is the number of particles in a cluster) holds for particles up to about three times the wavelength of incident light.
The authors also describe a optical pulse particle size analyzer for measuring cluster size distribution. Clusters are passed, single file, through an optical flow cell, which is uniformly illuminated by a focused laser beam. As the clusters pass through the illuminated volume they scatter light. This scattered light is collected at low angles (3.degree.) and imaged on the surface of a photomultiplier tube. The generated photocurrent pulses are then passed through an analog square root amplifier and finally sorted on a multichannel pulse-height analyzer. The resulting histogram consists of a series of linearly spaced peaks--each corresponding to a different size n-mer.